Testing the protein-leverage hypothesis using population surveillance data.

It is hypothesized that humans exhibit 'protein leverage' (PL), whereby regulation of absolute protein intake results in the over-consumption of non-protein food on low percentage protein diets. Testing for PL using dietary surveillance data involves seeking evidence for a negative association between total energy intake and percentage energy from protein. However, it is unclear whether such an association might emerge without PL due to the structure of intake data (protein and non-protein intakes have different means and variances and covary). We derive a set of models that describe the association between the expected estimate of PL and the distributions of protein and non-protein intake. Models were validated via simulation. Patterns consistent with PL will not emerge simply because protein intake has a lower mean and/or variance than non-protein. Rather, evidence of PL is observed where protein has a lower index of dispersion (variance/mean) than non-protein intake. Reciprocally, the stronger PL is the lower the index of dispersion for protein intake becomes. Disentangling causality is ultimately beyond the power of observational data alone. However, we show that one can correct for confounders (e.g. age) in generating signals of PL, and describe independent measures that can anchor inferences around the role of PL.